Question

determine a área de um triângulo cujos os lados medem:​

Answer 1

Para calcular a área de um triângulo qualquer, sendo dadas as medidas dos seus três lados, podemos utilizar a formula de Heron:

$Area~=~\sqrt{p\cdot(p-a)\cdot(p-b)\cdot (p-c)}\\\\\\Onde:~~~\left\{\begin{array}{ccl}a,~b,~c&:&Medidas~dos~lados\\p&:&Semiperimetro~~ \left(p~=~\dfrac{a+b+c}{2}\right)\end{array}\right$

b)

$p~=~\dfrac{6+8+10}{2}\\\\\\p~=~\dfrac{24}{2}\\\\\\\boxed{p~=~12~cm}$

$Area~=~\sqrt{12\cdot(12-6)\cdot(12-8)\cdot(12-10)}\\\\\\Area~=~\sqrt{12\cdot(6)\cdot(4)\cdot(2)}\\\\\\Area~=~\sqrt{12\cdot(6)\cdot8}\\\\\\Area~=~\sqrt{12\cdot48}\\\\\\Area~=~\sqrt{576}\\\\\\\boxed{Area~=~24~cm^2}$

c)

$p~=~\dfrac{12+16+20}{2}\\\\\\p~=~\dfrac{48}{2}\\\\\\\boxed{p~=~24~cm}$

$Area~=~\sqrt{24\cdot(24-12)\cdot(24-16)\cdot(24-20)}\\\\\\Area~=~\sqrt{24\cdot(12)\cdot(8)\cdot(4)}\\\\\\Area~=~\sqrt{24\cdot(12)\cdot32}\\\\\\Area~=~\sqrt{24\cdot384}\\\\\\Area~=~\sqrt{9216}\\\\\\\boxed{Area~=~96~cm^2}$

d)

$p~=~\dfrac{3+4+5}{2}\\\\\\p~=~\dfrac{12}{2}\\\\\\\boxed{p~=~6~cm}$

$Area~=~\sqrt{6\cdot(6-3)\cdot(6-4)\cdot(6-5)}\\\\\\Area~=~\sqrt{6\cdot(3)\cdot(2)\cdot(1)}\\\\\\Area~=~\sqrt{6\cdot(3)\cdot2}\\\\\\Area~=~\sqrt{6\cdot6}\\\\\\Area~=~\sqrt{36}\\\\\\\boxed{Area~=~6~cm^2}$

$\Huge{\begin{array}{c}\Delta \tt{\!\!\!\!\!\!\,\,o}\!\!\!\!\!\!\!\!\:\,\perp\end{array}}Qualquer~d\acute{u}vida,~deixe~ um~coment\acute{a}rio$